Khot and Shinkar (RANDOM, 2016) recently describe an adaptive, $O(n\log(n)/\varepsilon)$-query tester for unateness of Boolean functions $f:\{0,1\}^n \mapsto \{0,1\}$. In this note we describe a simple non-adaptive, $O(n\log(n/\varepsilon)/\varepsilon)$ -query tester for unateness for functions over the hypercube with any ordered range.

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Various combinatorial/algebraic parameters are used to quantify the complexity of a Boolean function. Among them, sensitivity is one of the simplest and block sensitivity is one of the most useful. Nisan (1989) and Nisan and Szegedy (1991) showed that block sensitivity and several other parameters, such as certificate complexity, decision ... more >>>

We prove that for every $n$ and $1 < t < n$ any $t$-out-of-$n$ threshold secret sharing scheme for one-bit secrets requires share size $\log(t + 1)$. Our bound is tight when $t = n - 1$ and $n$ is a prime power. In 1990 Kilian and Nisan proved ... more >>>